The rapid increase of the demand for wireless applications has stimulated tremendous research efforts in developing systems that support reliable high rate transmissions over wireless channels. However, these developments must cope with challenges such as multipath fading, time varying nature of the wireless channel, bandwidth restrictions and handheld devices power limitations. Space-time transmission techniques have been proven to combat the detrimental efforts of the multipath fading. Unfortunately, the large delay spreads of frequency selective fading channels destroy the orthogonality of the received signals which is critical for space-time coding. Consequently, the techniques are only effective over frequency flat block fading channels. Orthogonal frequency division multiplexing (OFDM) has also shown to combat the multipath fading. A space-time OFDM (ST-OFDM) and space-frequency OFDM (SF-OFDM) have been proposed as an effective way to combat the frequency selectivity of the channel. Moreover, SF-OFDM can be applied to fast fading channel wherein the channel doesn't need to be constant for at least two block transmission as it is usually required for ST-OFDM scheme. OFDM is a multicarrier communication technique, with which a single data stream is transmitted over a number of lower rate subcarriers. A multicarrier signal consists of a number of independent modulated subcarriers that can cause a large peak-to-average PAPR when the subcarriers are added up coherently. Also OFDM suffer from phase noise and the frequency offset problems. Therefore, to combat the frequency selectivity of the channel, an alternative solution for OFDM was proposed that utilizes single carrier transmission with frequency domain equalization. In parallel to ST-OFDM scheme, a space-time single carrier (ST-SC) transmission scheme was proposed in that requires the channel to be same for at least two block periods.
Although many high rate wireless communication method and systems have been proposed, none provide a space-frequency single carrier (SF-SC) technique which doesn't require the channel to be the same for two block periods, and hence beneficial for fast fading channel. Prior methods and systems do not use a single carrier transmission technique that implements space-frequency block coding with additional frequency diversity as shown in the next section.